Problem: Multiply the following complex numbers: $({-4-5i}) \cdot ({-4-4i})$
Solution: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-4-5i}) \cdot ({-4-4i}) = $ $ ({-4} \cdot {-4}) + ({-4} \cdot {-4}i) + ({-5}i \cdot {-4}) + ({-5}i \cdot {-4}i) $ Then simplify the terms: $ (16) + (16i) + (20i) + (20 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 16 + (16 + 20)i + 20i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 16 + (16 + 20)i - 20 $ The result is simplified: $ (16 - 20) + (36i) = -4+36i $